Research map / Learning theory and algorithms / Kernels and regression theory
On the Discrimination-Generalization Tradeoff in GANs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a discriminator set whose linear span is dense in bounded continuous functions | Neural distance · Borel probability measures | discrimination | Helped |
| Use a single ReLU neuron with the stated bounded parameter set | Neural distance · Compact subsets of R^d | discrimination | Helped |
| Restrict discriminator complexity | GAN training evaluated by neural distance · I.i.d. samples of size m | generalization error: 2 R_m^{(\mu)}(\CalF) + 2 \Delta \sqrt{\frac{2 \log(1/\delta)}{m}} + \epsilon | Helped |
| Use a single-ReLU neural discriminator instead of bounded Lipschitz distance as the objective | GAN · Unit ball in R^d | neural-distance generalization rate: O(m^{-1/2}) | Helped |
| Use total variation distance as the training objective | GAN · Uniform distribution on X | total variation generalization: R_m^{(\mu)}(\CalF) = 2; d_\mathrm{TV}(\mu, \hat{\mu}_m) = 2 | Hurt |
| Require positive densities and discriminator compatibility with generator log-density ratios | GAN evaluated by KL divergence · Distributions with positive densities | KL divergence: \mathrm{KL}(\mu, \nu_m) \leq \Lambda_{\mathcal{F}, \mathcal{G}}~ \big ( 2 R_m^{(\mu)}(\mathcal{F}) + 2 \Delta \sqrt{2 \l | Helped |
| Use bounded Lipschitz distance rather than total variation distance | GAN generalization analysis · Convex bounded set in R^d | generalization rate: R_m^{(\mu)}(\CalF) \leq m^{-1/d} for d>2; O(m^{-1/d}) | Mixed |
| Add an output activation function to the discriminator | Neural φ-divergence · Borel probability measures | discrimination | Helped |
| Require bounded discriminators | Neural distance · I.i.d. samples of size m | generalization error: 2 R_m^{(\mu)}(\CalF) + 2 \Delta \sqrt{\frac{2 \log(1/\delta)}{m}} + \epsilon | Helped |
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